Exact solutions for one-dimensional (1D) plasma dynamics in an rf trap are known when space charge effects are neglected [K. Shah and H. S. Ramachandran, Phys. Plasmas 15, 062303 (2008)]. In this work, weak space charge effects in an rf trap are considered. An analytic expression for the time varying distribution function of the 1D plasma is obtained. It is shown that the plasma is a Maxwellian up to the lowest order in nonlinearity and that the spatially constant temperature periodically oscillates in time at the same rate as the rf frequency. It was shown by Krapchev [Phys. Rev. Lett. 42, 497 (1979)] that the time averaged distribution function is double humped with respect to velocity beyond a certain threshold in space. The time average of the complete time varying distribution function is obtained and some of the predictions of Krapchev are recovered, while also finding discrepancies. The relationship between stroboscopic orbits and the time averaged ponderomotive orbit are obtained for such traps.

RF confined electron plasmas are of importance in Paul traps [W. Paul, Rev. Mod. Phys. 62, 531 (1990)]. The stability of such plasmas is unclear and statistical heating arguments have been advanced to explain the observed heating in such plasmas [I. Siemers et al., Phys. Rev. A 38, 5121 (1988)]. This study investigates the nature of a one-dimensional collisionless electron plasma that is confined by an rf field of the form [−B+Acos(ωt)]x, where x is the space coordinate and ω is the rf frequency. Nonlinearly exact solutions are obtained. The distribution function and the plasma density are obtained in closed form and have constant shapes with time varying oscillations. These oscillations are at the rf frequency and its harmonics, modulated by a low frequency related to the electron bounce time. The linear limit of weak fields is recovered. Analytic expressions are obtained for the required external field to make it consistent with prescribed distribution functions. These solutions remain valid even in the presence of collisions. Solutions involving multiple species are also obtained, though only for collisionless traps. It is found that the ponderomotive force response needs to be corrected to account for the temperature fluctuations. No stochastic heating is observed in this field configuration.

A one-dimensional plasma discharge is analyzed under steady state conditions. Using simple models for source and collisions, a first-order differential equation is obtained that simultaneously describes both the bulk and the presheath of the plasma. This equation is numerically solved in various regimes and physically interesting quantities such as the ratio of bulk to edge density and the size of the inertial terms in the bulk region are presented. Analytic expressions are obtained for profiles when collision frequency is assumed constant. Findings include nB/nSE∼2.5 for highly collisional systems, significant flow in the bulk plasma, and modified I–V characteristics.

Toroidal electron plasmas have remained less explored due to their poor confinement properties. Their equilibrium, stability, and confinement properties are therefore not entirely understood and continue to remain a topic of intense ongoing research. Large aspect-ratio theory suggests poor confinement in toroidal devices can be overcome by the application of a radial electric field; this has been verified successfully in some of the recent experiments. In the present paper, we report the longest confinement time without these external forces. Increasing the toroidicity has helped us to generate these forces intrinsically. To this end, a trap to confine electron plasmas has been created in a small aspect-ratio (≈1.6) torus. Electrons after being injected from a thermionic source are seen to remain confined with a purely toroidal magnetic field. The confinement time is far more than known single particle drift time scales. Importantly, it is in the absence of any external electric field, additional rotational transform, and/or magnetic fields, which, although not required, in principle, may appear essential particularly due to their role in improving confinement in some of the recent large aspect-ratio traps. The successful confinement in the small aspect-ratio limit has also led to several interesting observations: the evolution of the confined plasma is marked by an interesting nonlinear (large amplitude), electrostatic wave activity. Coherent, periodic, double peak oscillations result from a low-frequency E×B motion of a toroidal vortex in a plasma that closely leans against the inner wall. As many as 16 highly phase-coherent harmonics with dominant power in m=2 suggest that the mode is not merely a center-of-charge motion. Rather, a strong coupling of modes leads to a novel nonlinear state. The predominant energy is present in the shaping of the electron cloud (m=2) and not in the displacement of the center of charge (m=1) seen in large aspect-ratio traps. The absence of any power-law tail suggests absence of any turbulence, at least on time scales longer than the wall-probe resolution (40ns). The frequency, (around 100kHz at 200G) shows an unusual shear in time: it reduces as the mode evolves, but later increases as the mode dies.

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